Multiple sulfur isotope fractionation in hydrothermal systems in the presence of radical ions and molecular sulfur

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systems in the presence of radical ions and molecular sulfur

Maria Kokh, Nelly Assayag, Stéphanie Mounic, Pierre Cartigny, Andrey Gurenko, Gleb Pokrovski

To cite this version:

Maria Kokh, Nelly Assayag, Stéphanie Mounic, Pierre Cartigny, Andrey Gurenko, et al.. Multiple sulfur isotope fractionation in hydrothermal systems in the presence of radical ions and molecular sul- fur. Geochimica et Cosmochimica Acta, Elsevier, 2020, 285, pp.100-128. �10.1016/j.gca.2020.06.016�.

�hal-02905571�

Multiple sulfur isotope fractionation in hydrothermal systems in the presence of radical ions and molecular sulfur

Maria A. Kokh, Nelly Assayag, Stephanie Mounic, Pierre Cartigny, Andrey Gurenko, Gleb S. Pokrovski

PII: S0016-7037(20)30376-8

DOI: https://doi.org/10.1016/j.gca.2020.06.016

Reference: GCA 11808

To appear in: Geochimica et Cosmochimica Acta Received Date: 15 July 2019

Revised Date: 15 June 2020 Accepted Date: 19 June 2020

Please cite this article as: Kokh, M.A., Assayag, N., Mounic, S., Cartigny, P., Gurenko, A., Pokrovski, G.S., Multiple sulfur isotope fractionation in hydrothermal systems in the presence of radical ions and molecular sulfur, Geochimica et Cosmochimica Acta (2020), doi: https://doi.org/10.1016/j.gca.2020.06.016

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1

2 Multiple sulfur isotope fractionation in hydrothermal

3 systems in the presence of radical ions and molecular

4 sulfur

5

6

7 Maria A. Kokh ¹ , Nelly Assayag ² , Stephanie Mounic ¹ , Pierre Cartigny ² ,

8 Andrey Gurenko ³ , and Gleb S. Pokrovski ¹ *

9

10

Groupe Fluids at Extreme Conditions (FLEX), Géosciences Environnement Toulouse, GET,

11 Université de Toulouse, CNRS, IRD, UPS, 14 avenue Edouard Belin, F-31400 Toulouse, France

12

13

Université de Paris, Institut de Physique du Globe de Paris, CNRS, F-75005 Paris, France.

14

15

Centre de Recherches Pétrographiques et Géochimiques (CRPG), 15 Rue Notre Dame des

16 Pauvres, F-54500 Vandœuvre-lès-Nancy, France

17 18

19 * Corresponding author: Phone: (33)-(0)5-61-33-26-18; fax: (33)-(0)5-61-33-25-60;

20 gleb.pokrovski@get.omp.eu

21

22 Revision 3

23 Geochimica et Cosmochimica Acta

24 15 June 2020

26 Keywords:

27 Trisulfur radical ion; disulfur radical ion, molecular sulfur; hydrothermal fluid; experiment; sulfur isotopes;

28 mass dependent fractionation (MDF); mass independent fractionation (MIF).

29

30 Abstract:

31 This study is aimed to evaluate the role played by the sulfur radical ions (S

and S

) and molecular sulfur 32 (S

) on sulfur isotope fractionation and to investigate if these species may leave an isotope fingerprint in 33 hydrothermal systems. For this purpose, we combined i) experiments using a hydrothermal reactor with 34 aqueous S

(S

)-S

-sulfate-sulfide fluids and pyrite across a wide range of temperatures (300-450°C), 35 pressures (300-800 bar), fluid acidity (4<pH<8) and with elevated total sulfur concentrations (0.1-1.0 mol/kg 36 fluid) favorable for formation of those polymeric sulfur species, ii) precise quadruple S isotope analyses of 37 the different S-bearing aqueous species in sampled fluids and in-situ precipitated pyrite, and iii) 38 thermodynamic modeling of sulfur aqueous speciation and solubility. Our results quantitatively confirm both 39 equilibrium and kinetic SO

-H

S and pyrite-H

S mass dependent fractionation (MDF) factors previously 40 established using extensive experimental and natural data from more dilute fluids in which polymeric sulfur 41 species are negligible. MDF signatures of S

measured in the sampled fluids of this study reveal different S

- 42 forming pathways such as i) breakdown on cooling of S

(and S

) and other chain-like S

polymers only 43 stable at high temperature and being isotopically identical to H

S; ii) cyclooctasulfur (S

, liquid or solid) 44 precipitating by recombination of sulfate and sulfide and/or by exchange with polysulfide dianions (S

) on 45 cooling and being slightly

S-enriched compared to H

S (by ~2 ‰ of 

S); and iii) a different type of S

46 resulting from thiosulfate irreversible breakdown and being highly

S-depleted (by ~12 ‰) relative to H

S.

47 Our data do not show any significant mass independent fractionation (MIF) of

S and

S, with 

S and 48 

S values of any S aqueous species and pyrite being within ±0.1 ‰ and ±1.0 ‰, respectively. Therefore, 49 under the investigated experimental conditions, the radical S

ion is unlikely to generate significant MIF in 50 the hydrothermal fluid phase and in pyrite and native sulfur precipitated therefrom. Our study supports the 51 existing interpretations of small 

S and 

S variations between sulfide/sulfate-bearing fluid and pyrite as 52 MDF in terms of reaction kinetics, different reaction pathways, and mass conservation effects such as mixing 53 of S reservoirs or Rayleigh distillation. Our data extend, across a wider range of sulfur concentration and 54 chemical speciation, the existing multiple S isotopes models that exploit such variations as a complement to 55 the traditional 

S tracer to monitor the approach to equilibrium and evolution of hydrothermal fluids.

56 57

58 Highlights:

59  Isotope signatures of sulfur species and pyrite have been studied in hydrothermal fluids.

60  MDF equilibrium and kinetic SO

-H

S and pyrite-H

S factors are quantified.

61  No MIF anomalies are detected in the presence of sulfur radical ions.

62  Isotope signature of molecular sulfur fingerprints the different mechanisms of S

formation.

63  Several environments offer potential for MIF generation in fluid-mineral systems.

65 1. INTRODUCTION

66

67 Fractionation among the four stable isotopes of sulfur (

S,

S,

S, and

S) has been used for tracing 68 various geological processes since 1960’s (e.g., Thode et al., 1961; Hulston and Thode, 1965). In most 69 chemical and biological reactions, the sulfur isotope ratios obey mass-dependent fractionations (MDF);

70 however, significant mass-independent fractionation (MIF) anomalies (

S >0.2‰)

were identified in 71 pyrite and barite from Archean sedimentary rocks likely caused by SO

photolysis in the atmosphere (e.g., 72 

S ≈ -4 to +14 ‰; Farquhar et al., 2000; Johnston, 2011; Philippot et al., 2012), and also in sulfide minerals 73 from a number of younger magmatic, hydrothermal and metamorphic rocks (e.g., Farquhar et al., 2002;

74 Bekker et al., 2009; Thomassot et al., 2009; Cabral et al., 2013; Young et al., 2013; Delavault et al., 2016;

75 Ripley and Li, 2017; LaFlamme et al., 2018a,b; Smit et al., 2019), which were interpreted as the 76 reworking/recycling of Archean supracrustal rocks. These anomalies contrast with very small 

S values, 77 which are likely generated through MDF processes in low-temperature biological and inorganic sulfur redox 78 reactions in solution or at the mineral surfaces (typically <0.15‰, Farquhar and Wing, 2003; Ono et al., 79 2006, 2007; Farquhar et al., 2007; Johnston, 2011). These MDF processes are quite well understood and 80 result from mass-conservation effects (mostly mixing and Rayleigh distillation). Earlier theoretical work 81 using quantum-chemistry modeling suggested that MIF could be generated by heterogeneous reactions 82 (Lasaga et al., 2008), which was, however, not supported by a subsequent study (Balan et al., 2009).

83 In most hydrothermal fluids studied so far in nature (e.g., Kamyshny et al., 2014; Stefansson et al., 84 2015; McDermott et al., 2015) and laboratory (e.g., Ohmoto and Lasaga, 1982; Syverson et al., 2015;

85 Meshoulam et al., 2016), relevant to active seafloor or surface geothermal systems and different shallow- 86 crust hydrothermal deposits, sulfur isotope fractionation between the different inorganic sulfur species such 87 as sulfate, sulfide, native sulfur, thiosulfate, and some organic thiol species has been interpreted by both 88 equilibrium and kinetic MDF. This type of fractionation can only generate small deviations of

S isotope 89 abundance from the classical MDF dependence (

S <0.05 ‰). In contrast, large 

S anomalies (from -1.1 90 to +13.0‰) were reported in thermochemical sulfate reduction (TSR) reactions in hydrothermal experiments 91 in the presence of amino-acids (Watanabe et al., 2009; Oduro et al., 2011). TSR phenomena were also 92 invoked to explain the 

S record in Paleoproterozoic black shales at Talvivarra, Finland (-0.6<

S<1.3%, 93 Young et al., 2013).

94 In the light of the large variety of sulfur isotope fractionation patterns exemplified above, detailed 95 knowledge of sulfur chemical speciation in the fluid phase is required for understanding sulfur isotope

1

Variations of S isotope ratios (normalized to the most abundant

S isotope) are conventionally expressed in the -notation relative to the V-CDT standard (Vienna-Cañon Diablo Troilite meteorite; Ding et al., 2001):



S (in ‰) = [(

S/

S)

/(

S/

S)

– 1]×1000, where x denotes 3, 4 or 6 for

S,

S, and

S, respectively.

MDF means that isotope ratios are proportional to the mass difference between isotopes yielding the relationships: 

S ≈

(0.515±0.005)×

S, and 

S ≈ (1.89±0.02)×

S (e.g., Urey, 1947). MDF refers to isotope compositions deviating from this mass

scaling law (i.e. 

S ≈ 

S – 0.515×

S; see section 2.5 for details and rigorous equations).

96 fractionation, both MDF and MIF, in natural processes involving fluids. The major chemical forms of sulfur 97 are known to be sulfate and sulfide (and sulfur dioxide and hydrogen sulfide in gas phase), which have been 98 extensively studied over the last decades. However, recent discoveries of the sulfur radical ions S

and S

99 in geological fluids (Pokrovski and Dubrovinsky, 2011; Pokrovski and Dubessy, 2015) may lead to re- 100 evaluate our vision of a number of geochemical processes in which sulfur is involved. For example, sulfur 101 radicals enhance gold and platinum solubility in hydrothermal fluids involved in porphyry and orogenic 102 deposit genesis (Pokrovski et al., 2015; 2019; Laskar et al., 2019). These radicals could also contribute to 103 redox changes in the subcontinental lithospheric mantle by slab-liberated S-bearing fluids in subduction 104 zones thereby affecting the sulfur release and metallogenic potential of the arc magmas (e.g., Rielli et al., 105 2017; Frimmel, 2018; Colin et al., 2020). At shallow-crust conditions, the S

ion was hypothesized to be a 106 reaction intermediate controlling the kinetics of TSR processes and associated sulfur isotope fractionations 107 (Truche et al., 2014; Pokrovski and Dubessy, 2015; Barré et al., 2017). The particular properties of S

make 108 it different from the ‘traditional’ sulfur species and, therefore, might be responsible for MIF

S anomalies 109 found in sulfides from hydrothermal settings and during TSR phenomena evoked above. This is because S

110 exhibits a magnetic moment due to a free electron, potentially enabling MIF, contrary to traditional sulfur 111 molecules and ions (Buchachenko, 2001). Furthermore, S

is a structural and electronic analog of ozone 112 (O

) and its radicals exhibiting large

O MIF anomalies due to symmetry effects (e.g.,

O

O

O vs 113

O

O

O), which is a general quantum-level control potentially applicable to other triatomic molecules and 114 radicals (Gao and Marcus, 2001; Babikov et al., 2003; Chakraborty et al., 2013; Reinhardt and Robert, 2013).

115 The major challenge in studying S

and S

is that they are only stable and sufficiently abundant in aqueous 116 solution at elevated temperatures and are not preserved on cooling/quench by very rapidly decomposing into 117 traditional sulfur species such as sulfide, sulfur, polysulfides, and/or sulfate (Chivers and Elder, 2013;

118 Pokrovski and Dubessy, 2015 and references therein).

119 Along with S

and S

, another previously disregarded sulfur species in hydrothermal fluids, is a 120 form of polymeric molecular sulfur (S

, where n is undetermined number of uncharged S atoms in chain- 121 like polymers), which has been identified by solubility and in-situ Raman spectroscopy measurements in S- 122 rich solutions at >200°C (Dadze and Sorokin, 1993; Pokrovski and Dubessy, 2015; Barré et al., 2017), but 123 its effect on both sulfur redox kinetics and isotope fractionation remains unexplored. This form of molecular 124 sulfur is different from the previously recognized aqueous cyclo-octasulfur S

(e.g., Kamyshny, 2008;

125 Pokrovski and Dubessy, 2015). Similarly to S

, S

is not preserved on cooling in its original state, by 126 transforming to native sulfur, molten or solid (S

, composed of S

rings), which is a common low- 127 temperature (<150°C) product of S-bearing fluids both in laboratory and natural hydrothermal-volcanic 128 settings. Therefore, native sulfur may potentially record, through its isotope signature, processes of sulfur 129 species transformation in fluids under elevated T-P conditions inaccessible to direct observation/sampling.

130 Such processes include disproportionation of magmatic SO

(e.g., Kusakabe et al., 2000; Kouzmanov and

131 Pokrovski, 2012), TSR reactions (Barré et al., 2017), or S

and S

transformations on cooling (e.g.,

132 Pokrovski and Dubessy, 2015). In this article, these different uncharged polymeric molecular sulfur forms 133 are collectively termed as ‘S

’.

134 In an attempt to bring quantitative constraints on the role played by the trisulfur (and disulfur) radical 135 ion and polymeric molecular sulfur on S isotope fractionation in hydrothermal environments, we combined 136 i) experiments in S

(S

)-S

-sulfate-sulfide hydrothermal fluids, ii) precise analyses of the multiple sulfur 137 isotope ratios in the different sulfur aqueous forms (sulfate, sulfide and S

) and coexisting pyrite, and iii) 138 thermodynamic modeling of sulfur aqueous speciation and solubility. The results contribute to better 139 understanding of complex sulfur isotope fractionation processes in both ancient and modern hydrothermal 140 systems relevant to various types of metal ore deposits formed by S-bearing fluids within the Earth’s crust.

141

142 2. MATERIALS AND METHODS

143 2.1. Experimental strategy and conditions

144

145 Four experiments were conducted in synthetic aqueous sulfate-sulfide fluids from 300 to 450°C and 146 from ~300 to ~700 bar to investigate both kinetic and equilibrium sulfur isotope fractionation over a wide 147 range of S

concentrations (from <0.0001 to ~0.1 moles S per kg of fluid (m), Table 1). Aqueous thiosulfate 148 solutions K

S

O

(-HCl-KOH) served as the source of sulfur, following the same approach as recent in-situ 149 Raman spectroscopy studies that identified S

, S

and S

(Pokrovski and Dubessy, 2015). Potassium was 150 preferred to Na which forms at elevated temperatures a poorly soluble Na

SO

solid compared to K

SO

151 ( Linke and Seidell, 1965). Thiosulfate breaks down in aqueous solution on heating above 150°C, producing 152 dominantly sulfate and sulfide

153 S

O

+ H

O = SO

+ H

S (1)

154 Adding acid (HCl) or base (KOH) allows enhanced formation of protonated (HSO

) or deprotonated (HS

) 155 species, respectively, enabling acidity buffering

156 SO

+ H

= HSO

(2)

157 H

S = HS

+ H

(3)

158 Alternatively, acidity buffering at slightly acidic pH values may also be achieved by using alkali 159 aluminosilicate mineral assemblages, such as quartz-muscovite-microcline, which was used in one of our 160 experiments (m22, see below). Furthermore, equilibria between sulfate and sulfide at elevated temperatures 161 impose oxygen fugacity (f

), which typically ranges, depending on pH, from HM-2 to HM+2 (where HM 162 denotes the logf

value of the conventional hematite-magnetite mineral buffer):

163 H

S + 2 O

= SO

+ 2 H

(4)

164 The formation of S

in such sulfate-sulfide solutions can be formally described by the reaction

165 19 H

S + 5 SO

+ 2 H

= 8 S

+ 20 H

O (5)

166 This reaction implies that the abundance of S

is controlled by total S concentration (S

, which is

167 proportional to the sum of the dominant sulfate and sulfide), solution pH, and the H

S/SO

ratio (and therefore

168 oxygen fugacity), with a maximum abundance at a given set of T, S

and pH at a H

S/SO

ratio of 19/5.

169 Note that this formal reaction in no way reflects the mechanisms of S

formation and breakdown, but only 170 illustrates the fundamental thermodynamic controls on the S

equilibrium concentration in solution. In 171 addition to the above S species produced by reactions (1) to (5), and depending on S and K total content, pH 172 and T-P conditions, variable amounts of sulfate and sulfide ion pairs with K

, SO

, S

(both aqueous and 173 molten), disulfur ion S

, and polysulfide dianions S

will also form.

174 The concentrations of all these species can be estimated using available thermodynamic data (see 175 section 2.6 and Table A2.1 for discussion and data sources). Figure 1 shows the calculated equilibrium 176 distribution of the different sulfur species, using the best up-to-date thermodynamic data (but see section 177 2.6), in K

S

O

aqueous solutions over the T-P-S

-pH-redox range of this study, and Table 1 overviews the 178 composition and different steps of the conducted experiments. In this manuscript, all pH values are 179 thermodynamically calculated at the corresponding T-P-composition. Two exploratory runs (m22 and m29) 180 at 350°C in acidic (pH ~4.5 at experimental T-P) and alkaline (pH ~7.3) solutions were designed to examine 181 S isotope fractionation in a S

-rich (~0.07 m S in the form of S

) and S

-poor (<0.001 m S) fluids, 182 respectively. A more elaborated experiment (m32) consisted of two succeeding steps in slightly alkaline S

183 - poor conditions (~0.005 m S) at two contrasting temperatures, 300 and 450°C, followed by an acidification 184 of the fluid at 450°C to increase S

concentration by a factor of 10 (~0.04 m S). In addition, the S

may 185 also be present at such elevated temperatures (Fig. 1b; Pokrovski and Dubessy, 2015; Pokrovski et al., 2019).

186 The last step of the three experiments above was conducted in the presence of pyrite (plus barite in m22) 187 whose precipitation was induced by injecting, in-situ into the reactor, an FeCl

(plus BaCl

in m22) aqueous 188 solution, thus simulating pyrite precipitation in natural hydrothermal fluids. Finally, a fourth experiment 189 (m33) was conducted at 300°C at near-neutral pH (~5.3) by progressively diluting with water the initial 190 K

S

O

-bearing fluid leading to a decrease of S

concentration by a factor of 10 (from ~0.07 to 0.008 m S), 191 to examine the effect of changing of S

abundance on sulfur isotope fractionation.

192 Our experimental systems offer a good analog for natural S-rich fluids in arc-related magmatic–

193 hydrothermal systems hosting porphyry, skarn and epithermal Cu-Au-Mo deposits, which are characterized 194 by typical temperatures of 250-500°C, pressures of 100-1000 bar, a wide pH (3-8) and redox (HM±2) ranges, 195 typical salinities of 5-15 wt% of NaCl+KCl, the coexistence of sulfate and sulfide in a wide range of 196 concentrations (from ~0.01 to a few wt% S), and the ubiquitous presence of pyrite (Einaudi et al., 2003;

197 Kouzmanov and Pokrovski, 2012). Furthermore, the isotope fractionation patterns obtained in this study are 198 also relevant to other hydrothermal settings and ore-deposit contexts that are all characterized by the presence 199 of S-bearing fluids and iron sulfide minerals (e.g., seafloor geothermal systems, orogenic and sedimentary 200 basin metal deposits).

201

202 2.2. Experimental setup

203

204 The runs were conducted using a Coretest reactor (Fig. 2) equipped with a flexible gold inner cell 205 with a Ti 2-µm frit filter in its head, i.e. analogous to Seyfried et al. (1987) and Rosenbauer et al. (1993) and 206 recently adapted to multicomponent and S-rich systems as described previously (Pokrovski et al., 2015; Kokh 207 et al., 2017). The gold cell (120-180 cm

of initial volume) is inserted into a high-pressure vessel (~1000 cm

208 volume, type 316 SS, stainless steel), which is filled with water as a pressure medium controlled by a gas- 209 driven pump, and placed into an electrically heated (±1°C) rocking furnace. An ultrafast sampling device, 210 analogous to that of Seewald and Seyfried (1990), consists of a titanium tube attached to two high-pressure 211 titanium valves and a rigid titanium vial (~2.5 cm

) tightly assembled to the second valve. The device enables 212 an almost instantaneous (<1 s) transfer into the vial of a portion of the fluid phase pushed by the internal 213 pressure from the reactor. This design prevents sulfur precipitation or degassing (see Kokh et al., 2017 for 214 details), which would have inevitably occurred in S-bearing systems using traditional sampling procedures.

215 Prior to experiments, the gold cell was cleaned with HNO

and annealed at 380°C for 1 h to allow for a 216 greater malleability and deformation.

217 During an experiment, fluids were periodically sampled and processed as described in sections 2.3 218 and 2.4. In the course of experiments m32 and m33, aqueous HCl or pure water were injected into the cell, 219 initially loaded with a thiosulfate solution, using a calibrated capstan pump (total volume = 12 cm

). This 220 injection allows controlled changes of the fluid pH and S

concentration and, consequently, the sulfur 221 speciation (in particular, the amount of S

and S

, see Table 1 and Fig. 1). Precipitation of pyrite (together 222 with barite in m22), in the final stage of three experiments (m22, m29 and m32), was induced by injection 223 into the reactor of an FeCl

(-BaCl

) aqueous solution in amounts not exceeding those of aqueous sulfide.

224 Then the fluid composition continued to be monitored by periodic sampling, and the solid was finally 225 recovered upon complete cooling of the reactor.

226

227 2.3. Chemical analyses of sampled fluids

228

229 Because the complex sulfur speciation at elevated T-P strongly evolves upon fluid cooling (Fig. 1d), 230 the original species identity and distribution cannot be adequately recovered in quenched samples. Therefore, 231 special procedures are required for separation and preservation of the different sulfur forms for chemical and 232 isotope analyses. These procedures are based on improved methods developed in our previous studies of S- 233 rich fluid systems (e.g., Pokrovski et al., 2008; Kokh et al., 2016). Each sampling session comprised multiple 234 samples of the fluid phase (usually 5, amounting 0.5 to 1.0 g each), directly taken into specific aqueous 235 reagents (concentrated solutions of I

, Cd(CH

COO)

, Zn(CH

COO)

, NH

) placed in the sampling vial to 236 allow for quantitative recovery and preservation of the different forms of sulfur, as well as dissolved chloride, 237 potassium, iron and gold (Table A1.1). Total aqueous sulfur (S

) was analyzed in samples taken into aqueous 238 ammonia (28 wt% NH

) by inductively coupled plasma - atomic emission spectrometry (ICP-AES) and high- 239 performance liquid chromatography (HPLC) after complete oxidation by hydrogen peroxide (30 wt%

240 aqueous H

O

) of all S forms to sulfate. Total aqueous chloride was also analyzed by HPLC in the same NH

241 and H

O

-treated samples. Total reduced sulfur (S

, comprising H

S/HS

/KHS, S

and, eventually, SO

242 and unreacted thiosulfate) was trapped in HCl aqueous solution containing an excess of iodine over sampled 243 sulfur, and quantified by titration of the remaining I

by a standard thiosulfate solution, since all these reduced 244 S species react with I

(e.g., Charlot, 1966; Dadze and Sorokin, 1993). Sulfide-type sulfur (S

, comprising 245 H

S, HS

and KHS) was separated from the other sulfur forms by sampling the fluid into a cadmium acetate 246 solution of near-neutral pH (~6), which results in quantitative precipitation of all sulfide species as poorly 247 soluble Cd sulfide (CdS solubility is <mol Cd/kg fluid), followed by iodometric titration in an I

-HCl 248 solution. Oxygen gas in the air space of the vial before sampling is less than 0.001 mmol/L, compared to 10s 249 to 100s mmol/L of potentially oxidizable S species in the fluid (e.g., H

S), so that oxidation by air is 250 negligible. Sulfate-type aqueous sulfur (S

, comprising SO

, HSO

, and their K

ion pairs, existing at 251 experimental T-P conditions, Fig. 1) was quantified by HPLC as the SO

ion in water-diluted near-neutral 252 pH acetate solutions, after removal of sulfide as CdS precipitate by centrifugation. The presence of thiosulfate 253 in the supernatant was also checked by HPLC, but could not be quantified.

254 Molecular sulfur was separated from other S species as hexane extracts (hereafter S

) collected 255 from samples trapped into Cd acetate solution followed by removal of CdS via centrifugation. The hexane 256 fraction was then analyzed for S

by UV spectrometry at a wavelength of 264 nm calibrated using reference 257 solutions prepared by dissolving a given amount of native sulfur in hexane. The analytical uncertainty on the 258 S

concentration determination in our systems is typically ±50%, mostly because impurities common in our 259 chemically complex samples (including acetate and its decomposition products that may partition into 260 hexane) absorb in the same UV range. All vials and tubes were also rinsed with hexane after recovery of each 261 sampled solution, and analyzed for S

, which has always been found below the detection limit (<0.0001 m 262 S). An independent way for estimating S

concentrations in the sampled fluid was using sulfur mass balance 263 between S

and the sum of sulfate and reduced sulfur (hereafter S

), because S

does not react with 264 iodine and does not precipitate with Cd or Ba acetate.

265 Concentrations of potassium, gold and iron were determined by ICP-AES and, selectively, by flame 266 atomic absorption spectrometry (FAAS), after the NH

sample treatment with aqua regia. This treatment 267 consists of i) gentle evaporation of the sample on hot plate (60-80°C) in a cleaned Teflon vial (Savilex ®), 268 ii) reaction of the residue with 2 g of hot aqua regia in the closed vial (at 120°C for 2h), followed by iii) 269 gentle evaporation of solution (at 60-70°C) to 0.2-0.3 g, and iv) dilution of the remaining solution by ultra- 270 pure 0.5 wt% HCl - 1.5wt% HNO

in water. More details on the chemical procedures and associated 271 uncertainties are given in Kokh et al. (2016, 2017). The results of fluid analyses are reported in Table 2 and 272 shown as a function of run duration in Fig. 3.

273

274 2.4. Processing of sampled fluids for sulfur isotope analyses

275

276 The sulfur isotope ratios were analyzed (depending on the experiment) in the initial thiosulfate and

277 sampled aqueous sulfate, sulfide and molecular sulfur (if available), and in the precipitated pyrite recovered

278 after the run. Like for the chemical analyses described above, the challenge was to accurately separate the 279 different sulfur forms on sampling to avoid, as much as possible, both chemical recombination and isotope 280 exchange/mixing among these forms in our S-rich systems on cooling. The fluid sample treatment is 281 described as follows and summarized in Table A1.1.

282 In an exploratory experiment (m22), sulfur samples were taken into an aqueous solution of zinc and 283 barium acetate, resulting in simultaneous precipitation of ZnS and BaSO

in the sampling vial. However, 284 difficulties were encountered when converting ZnS to H

S from the fine-grained ZnS-BaSO

mixture that 285 prevented ZnS, being armored by BaSO

, to quantitatively react with the HCl solution, resulting in low yields.

286 Consequently, the experimental protocol was changed in the subsequent experiments. In runs m29, m32, and 287 m33, aqueous sulfide was trapped as ZnS by placing 1.0-1.5 mL of 1 m zinc acetate solution into the sampling 288 vial. The formed ZnS precipitate was centrifuged (3800 rpm for 15 min) to separate it from the solution, 289 washed with deionized water and dried at 90°C for subsequent isotope analyses. After centrifugation, the 290 supernatant solution was reacted with 1.5 mL of 1 m barium acetate to precipitate BaSO

, which was then 291 centrifuged, washed, dried similarly to the ZnS precipitate, and reserved for isotope analyses.

292 Molecular sulfur S

was separated by extraction into hexane after precipitating H

S as CdS when 293 sampling the fluid directly into a 1 mL of 1 m cadmium acetate solution. This procedure prevents i) isotope 294 exchange between S

and H

S/HS

prone to rapid re-equilibration, and ii) possible recombination of sulfate 295 and sulfide to form additional S

. Despite all these precautions, native sulfur might still partly precipitate, 296 especially in S-rich acidic solutions, during the fluid passage through the sampling tubes and valves before 297 reaching the vial with the trapping reagent, and thus get transferred into the vial together with the fluid.

298 Although the different origins and formation mechanisms of S

in the sampled fluid cannot be distinguished 299 by bulk S

chemical analyses, their isotopic composition is expected to reflect those mechanisms. The 300 supernatant containing sulfate and S

was separated from the CdS precipitate by centrifugation (3800 rpm 301 for 15 min), filtered (0.45 µm) and placed into a glass flask with 30 mL of hexane and 10 mL of glycerol (the 302 latter was used to protect the eventually remaining thiosulfate from oxidation that might lead to additional 303 formation of molecular sulfur; Dadze and Sorokin, 1993). The aqueous solution and the hexane phase were 304 allowed to react for at least 48 h to enable the complete extraction of S

into the hexane phase, as checked by 305 time-dependent analyses. The S

-bearing hexane fraction was then recovered and analyzed for S

by UV-Vis 306 spectrometry (section 2.3). After the UV analysis, the hexane was gently evaporated at 50°C and the 307 precipitated sulfur was saved for isotope analyses.

308 The sulfur isotope composition of the initial thiosulfate was measured separately in its sulfane (S

) 309 and sulfonate (S

) parts according to the slightly modified protocols of Uyama et al. (1985) and Syverson et 310 al. (2015). An aqueous 0.1 m AgNO

solution was used to precipitate the sulfane sulfur as Ag

S from an 311 aqueous 0.05 m K

S

O

solution. The supernatant was separated from the precipitate by centrifugation and 312 reacted with an excess of barium acetate to precipitate the sulfonate part as BaSO

, which was then recovered 313 after centrifugation.

314

315 2.5. Quadruple sulfur isotope analyses and isotope standardization and notation

316

317 Measurements of the four stable sulfur isotope ratios were realized with a gas source Ion Ratio Mass 318 Spectrometer (IRMS) Thermo Finnigan MAT 253 at the Institut de Physique du Globe de Paris (IPGP) as 319 described by Labidi et al. (2012). Samples of ZnS, BaSO

and S

were converted to solid silver sulfide (Ag

S) 320 using established techniques (Thode et al., 1961; Canfield et al., 1986; Labidi et al., 2012). The obtained 321 Ag

S was in turn quantitatively converted to sulfur hexafluoride gas (SF

) purified cryogenically by 322 distillation and by gas chromatography before being introduced into the spectrometer (Appendix A1 for 323 details). Procedural blanks, associated with sulfur conversion into Ag

S and subsequent Ag

S fluorination 324 and purification, are too low to be quantified (nano-molal levels). The S isotope composition of SF

(g) was 325 analyzed at mass-to-charge ratio values of 127, 128, 129, and 131 corresponding to the S

F

, S

F

, S

F

, 326 and S

F

ions, respectively (note that fluorine has a single stable isotope,

F, which avoids any mass 327 interference). Typical analytical errors of our measurements in a single session (2 standard deviations, 2 SD) 328 are 0.05 ‰, 0.01 ‰, and 0.18 ‰ for δ

S, Δ

S and Δ

S, respectively. Typical external reproducibility on 329 δ

S, Δ

S, and Δ

S among different sessions (conducted over >1 year and by several analysts) and parallel 330 chemical treatments of the same sampled fluid are 0.6 ‰, 0.02 ‰, and 0.35 ‰ (2 SD), respectively, as 331 estimated by four independent measurements of the pyrite sample from experiment m29.

332 All 

S, Δ

S and Δ

S data obtained in this study are reported relative to the V-CDT standard, which 333 is a virtual S isotope reference adopted instead of the previously used natural Cañon Diablo Troilite (CDT) 334 meteorite, that was found to be slightly isotopically heterogeneous (Ding et al., 2001). The V-CDT standard 335 was defined on the base of a homogeneous synthetic standard, IAEA-S-1 (Ag

S), with a δ

S value of -0.30‰

336 relative to V-CDT (Ding et al., 2001; references therein). Because there is presently no international standard 337 for δ

S and δ

S, in this study we anchored our

S and

S data to the V-CDT reference scale, for consistency 338 with the recent studies (Ono et al., 2007) assuming that δ

S

= -0.055±0.14 ‰, δ

S

= -1.37±0.5 ‰, 339 Δ

S

= 0.100±0.003 ‰, and Δ

S

= -0.8±0.1 ‰ (see also Geng et al., 2019 for a recent inter- 340 comparison). Note that this normalization has no consequences on calculations of isotope fractionation 341 factors between different sulfur species. Values of ∆

S and ∆

S were calculated according to Farquhar and 342 Wing (2003):

343 Δ

S

= 

S

– 1000 × [(1 + 

S

/1000)

– 1)] (6)

344 Δ

S

= 

S

– 1000 × [(1 + 

S

/1000)

– 1)] (7)

345 where 33 and 36 are adopted as 0.515 and 1.889, respectively (note that these values may vary by a few 346 ‰ in different equilibrium and kinetic isotope exchange reactions, Young et al., 2012). Isotope fractionation 347 between the different sulfur forms (here given for 

S) is expressed relative to aqueous sulfide analyzed as 348 ZnS:

349 1000×ln

≈ 

S

– 

S

(8)

350 where i denotes sulfate sulfur (collectively termed as SO

), molecular sulfur (S

) or pyrite (Py), and 

is the 351 conventional isotope fractionation factor between i-species and sulfide, (

S/

S)

/(

S/

S)

. The results 352 of S isotope analyses obtained in this study are reported in Tables 3 and 4 and plotted in Figs 5 to 8.

353

354 2.6. Chemical equilibrium calculations of aqueous sulfur speciation and solubility

355

356 Sulfur speciation and solubility in the fluid phase of the experimental systems were modelled using 357 available thermodynamic data, and the results were compared with the measured S species concentrations.

358 Calculations were performed using the HCh software package and associated Unitherm database, allowing 359 chemical equilibrium simulations in fluid-mineral systems (Shvarov, 2008; 2015), and accounting for non- 360 ideality of the fluid using the extended Debye-Hückel equation (Helgeson et al., 1981). The selection of 361 thermodynamic data sources was discussed in detail elsewhere (Pokrovski et al., 2015, 2019; Kokh et al., 362 2017), and will be only briefly summarized here.

363 The thermodynamic properties of the minerals, major fluid components, and most aqueous ionic 364 sulfur species were taken from the updated SUPCRT (Johnson et al., 1992), JANAF (Chase, 1998), and 365 USGS (Robie and Hemingway, 1995) databases, complemented by recent data for ionic sulfur forms 366 including S

(Pokrovski and Dubessy, 2015; references therein) using the revised and extended HKF 367 (Helgeson-Kirkham-Flowers) equation of state (Oelkers et al., 2009; Sverjensky et al., 2014; references 368 therein). The thermodynamic properties of the aqueous ‘gas-like’ sulfur nonelectrolytes, H

S, SO

, as well 369 as H

and O

, were adopted from Akinfiev and Diamond (2003) whose model provides a more accurate 370 description of such species over the T-P range relevant to our study (300-450°C; <1 kbar) than the SUPCRT 371 database, which was based on a more limited experimental dataset for derivation of the HKF model 372 coefficients for those species. The thermodynamic properties of the polysulfide ions (S

, where n is between 373 2 and 6) and aqueous S

at 300-450°C were taken from Pokrovski and Dubessy (2015); both types of species 374 were found to be negligible in the fluid at the elevated temperatures of our experiments (<0.001 m S; Fig. 1).

375 The S

radical ion, with a stability constant at 450°C and 700 bar from Pokrovski et al. (2019), was predicted 376 to account for ~0.01 m S in experiment m32, which is comparable to S

(Fig. 1b). However, the uncertainties 377 on such predictions are large (of an order of magnitude); furthermore, the S

ion is expected to be negligible 378 in our lower-T experiments since it has not been detected by Raman resonance spectroscopy below 450°C 379 (Pokrovski and Dubessy, 2015). The sources of thermodynamic properties of solid phases and aqueous 380 species used in the modeling are summarized in Table A2.1 and the results of calculations for typical 381 conditions of our experiments are shown in Fig. 1.

382 The missing species in these calculations are molecular sulfur polymers S

forming around 300°C 383 as detected by in-situ Raman spectroscopy (Pokrovski et Dubessy, 2015; Barré et al., 2017) and protonated 384 polysulfides (HS

), for which no thermodynamic data are currently available at elevated temperatures.

385 Estimations of Pokrovski and Dubessy (2015) suggest that S

equilibrium concentrations in thiosulfate

386 solutions more concentrated than those of our study (S

~2 m), attain maximum values of the order of 0.1-

387 0.2 m S around 300°C, and show sharply decreasing amounts with increasing T and/or decreasing S

388 concentration. However, considering the large errors of such estimates and possible multiple and likely out- 389 of-equilibrium origins of molecular sulfur found in the experiments of this study, quantification of S

390 equilibrium concentrations cannot confidently be made at present. Similarly, the amount of HS

cannot be 391 quantitatively assessed, but the absence of H-S vibrations in the Raman spectra of Pokrovski and Dubessy 392 (2015) and Barré et al. (2017) strongly suggests that their concentrations at T-P-pH conditions of our 393 experiments are likely to be too small to affect sulfur mass and isotope balance.

394 New data obtained in the course of this study allowed estimations of the amount and origin of S

at 395 elevated temperatures based of S

isotope signatures, and a revision of the stability of the major sulfate- 396 bearing species, KSO

(Fig. 1) based on the observation of K

SO

(s) precipitation in one experiment at 397 450°C (m32; section 4.1.1 and Appendix A3). The revised calculations, with corrected KSO

stability 398 constants, of equilibrium aqueous sulfate and sulfide concentrations for each experimental step will be 399 compared with their experimental counterparts (Fig. 4) and help to better constrain the interpretation of the 400 S isotope patterns.

401

402 3. RESULTS

403

404 3.1. Sulfur chemical speciation in the fluid phase

405

406 3.1.1. Experiments at 350°C (m22, m29)

407 Two experiments have been conducted at 350°C and 300-400 bar in acidic (0.5 m K

S

O

-0.14 m

408 HCl, pH

~4.5, run m22) and less concentrated slightly alkaline (0.2 m K

S

O

-0.09 m KOH, pH

~7.3,

409 run m29) solutions, corresponding to S

-rich (~0.07 m S) and S

-poor (~0.002 m S) compositions,

410 respectively. The concentrations of S species measured in these experiments are reported in Table 2 and their

411 evolution with time is shown in Fig. 3a,b. In both experiments, before FeCl

injection, sulfate and sulfide

412 represent the major fraction of dissolved sulfur. Reduced sulfur (S

) is slightly higher than sulfide, by 0.01

413 to 0.04 m S, in the acidic experiment (m22); the difference might be due to the presence of minor quantities

414 of SO

which is titrated by iodine together with sulfide. Reduced sulfur concentrations in the alkaline

415 experiment (m29) are identical to those of sulfide. There are no discernable changes of the species

416 concentration with time, suggesting that a chemical steady state is reached at this temperature within less

417 than a few days. Total S concentrations (S

) analyzed in the less concentrated alkaline-pH run (m29) match

418 the sum of S

and S

concentrations, implying an insignificant contribution of other S species that might

419 have been omitted by our analytical protocols (<0.03 m S). In contrast, significant imbalance (up to 0.3 m S)

420 between S

and the sum of S

and S

is apparent in the more concentrated acidic run (m22). This

421 imbalance (S

) is attributed to the presence of molecular sulfur S

in the sampled fluid, which can react

422 neither with iodine nor with cadmium or barium acetate. This S

may have multiple origins that will be

423 discussed in section 4. In the next step of both experiments, after the injection of FeCl

(m29) and KCl-FeCl

- 424 BaCl

(in m22), S

becomes largely dominated by sulfate given that a major part of reduced sulfur 425 precipitated as pyrite. Concentrations of S

are similar within errors to S

in m29, and are slightly higher 426 than S

in m22, likely due to the presence of minor amounts of SO

favored by acidic pH (Fig. 1).

427

428 3.1.2. Experiment at 300 and 450°C (m32)

429 More complete information about sulfur speciation has been gained in a subsequent experiment 430 conducted at 300 and 450°C (m32), with the development of a protocol for molecular sulfur analysis (see 431 section 2.3). This experiment was started in alkaline solution (0.5 m K

S

O

-0.3 m KOH pH

~7) at 300°C, 432 500 bar and run for 13 days (step m32/1); then the temperature was raised to 450°C and kept for 14 days 433 (pH

~8, m32/2). In a next step lasting 8 days (m32/3), an HCl solution was injected into the reactor 434 resulting in acidification (pH

~7), allowing a better identification of S

whose abundance is predicted 435 to increase at more acidic pH (Table 1, Fig. 1). In the final step (m32/4, lasting 8 days), a FeCl

solution was 436 injected, resulting in pyrite precipitation and further fluid acidification (pH

~6). Total K and S 437 concentrations steadily decrease at a molar K/S ratio close to 2 with time during the 300°C step (Fig. 3c and 438 A3.1). This decrease suggests the precipitation of K

SO

(s), which is known to have a retrograde solubility 439 with temperature (Pokrovski and Dubessy, 2015). Further decrease of S and K concentrations is observed as 440 the temperature was raised to 450°C, following by stabilization for ~1 week, suggesting an attainment of 441 steady state concentrations. The retrograde solubility of K

SO

(s) was apparent at the 450°C stage during a 442 temporary heating regulation problem before sample #6 (Table 2, Fig. 3c), causing the temperature to 443 decrease to ~260°C, and before sample #7, causing the temperature to increase to ~460°C. The solubility of 444 K

SO

(s) rapidly responded to these temperature changes by increasing above and then decreasing below the 445 steady-state values obtained in 2 previous samples #4 and #5 (Table 2; Fig. 3c, A3.1).

446 During the 300°C stage (m32/1), measured concentrations of sulfate and sulfide remained constant 447 over ~1 week, but their sum was inferior to that of S

by a factor of ~2 (Table 2, Fig. 3c), demonstrating the 448 presence of analytically unreactive molecular sulfur (S

). Concentrations of S

decreased by ~50%

449 accompanied by an increase in both sulfate and sulfide (in the 2

week), reflecting a slow and complex 450 kinetics of thiosulfate transformation. A fourth species contributing to aqueous S is the thiosulfate ion, S

O

, 451 which was detected by HPLC analyses in sample #1 solution after separation of ZnS. The presence of 452 undecomposed S

O

and/or its possible intermediate decomposition products (SO

) at this stage is also 453 independently confirmed by the systematically higher measured concentrations of S

compared to S

, 454 since both thiosulfate and sulfite are titratable by iodine, but do not precipitate with Cd or Zn.

455 The T rise to 450°C after that step resulted in a drop of S

concentrations by a factor of 5 to 10

456 as compared to the preceding sampling at 300°C (Fig. 3c). It should be noted that the S

values exhibit a large

457 scatter due to both analytical difficulties for measuring S

in hexane extracts (S

) and the use of mass-

458 balance relations (S

) for deriving close-to-zero values (~0.01 m S). Yet, despite the scatter, the S

459 concentrations appear, on average, quite similar to the S

ones (Fig. A4.3), yielding a mean value of

460 0.04±0.02 m S (1 SD) for S

concentration for the whole set of datapoints over the three steps at 450°C 461 (m32/2, 3, 4). Both types of S

data do not show any clear tendency as a function of elapsed time (Fig. 3c).

462

463 3.1.3. Experiment at 300°C and near-neutral pH (m33)

464 A fourth experiment was conducted at 300°C and 500 bar in 0.5 to 0.2 m K

S

O

solution at near- 465 neutral pH (pH

~5.3). This experiment was designed to better explore the effect of dilution resulting in 466 large changes in S

(and S

) concentrations without much changing the overall solution chemistry and 467 acidity. At the initial stage (~0.5 m K

S

O

, m33/1), sulfate and sulfide account for >60% of S

(Table 2).

468 There are no systematic changes within errors of their concentrations with time, suggesting that a chemical 469 steady state is reached. Likewise, there is no systematic difference between measured S

and S

470 concentrations, suggesting the absence of significant amounts (>0.02 m S) of reduced species other than 471 H

S/HS

(e.g., polysulfide ions, SO

, or undecomposed thiosulfate). In contrast, there is yet significant 472 imbalance (up to 30% S

) between S

and the sum of S

and S

, due to the presence of molecular 473 sulfur (S

, Table 2), as was also confirmed by direct analyses of S

. After the first injection of water, 474 this imbalance is significantly reduced as a result of dilution (to ~15% S

). After the second injection of 475 water, the S

fraction further decreased to become <5% S

after 1 week (Table 2, Fig. 3d). Like in experiment 476 m32, both types of S

datapoints (S

and S

) are quite scattered, but without any systematic trends 477 between them (Fig. A4.3).

478

479 3.2. Sulfur isotope ratios in the fluid phase and pyrite

480

481 In two exploratory experiments (m22 and m29), only a limited dataset could be obtained on S isotope 482 ratios of the different species (Table 3, Fig. A4.1 and A4.2). Most isotope data have been obtained on S

483 (trapped as ZnS) and S

(analyzed by the CRS treatment of the ZnS-BaSO

mixture in m22; Appendix A1).

484 Only few data points could be collected from S

(trapped as BaSO

) due to imperfections in separating 485 ZnS from BaSO

. The δ

S

and δ

S

values are consistently more negative, by 14-21 ‰, than the 486 δ

S

values; however, the paucity of the BaSO

data does not allow the identification of any systematic 487 trends with time.

488 A more extensive sulfur isotope data set has been obtained in experiment m32 (Table 3, Fig. 5a and

489 6). The isotope composition of sulfonate (O

-S-) and sulfane (-S) sulfur of the initial thiosulfate (which

490 decompose respectively to sulfate and sulfide according to reaction 1), evolves upon heating to 300°C, with

491 sulfate and sulfide becoming through time

S-enriched and

S-depleted, respectively. In other words, the

492 difference in 1000×ln

(δ

S

– δ

S

) at each given moment increases with time, yet without

493 reaching a steady state at 300°C (Fig. 5c). This evolution is mainly controlled by the increase in δ

S

,

494 whereas δ

S

remains constant within errors (Fig. 5a); this clearly indicates that at least a third S isotope

495 pool is being formed. After the temperature rise to 450°C, δ

S

values stay constant while δ

S

values

496 increase slightly (by <2‰ over 30 days), yielding a value 1000×ln

of 15.0±1.0 ‰ for the two last data 497 points after pyrite precipitation. Only three isotope compositional data points could be obtained for S

498 in this experiment. One data point from the first sample taken just after T change to 450°C (sample #4, Table 499 3) has an anomalously light isotope signature relative to sulfide (1000×ln

= -11.6 ‰). Such a low value 500 is unlikely to be an analytical artifact, since it is in good agreement with that calculated using sulfur mass 501 and isotope balance on sulfate and sulfide (Fig. 5a, Appendix A5). The two other S

isotope data points, 502 obtained in samples #8 and #9 taken respectively 2 and 5 days after the HCl injection at 450°C (stage m32/3), 503 show 1000×ln

values tending to zero. The isotope composition of the precipitated pyrite in this experiment 504 is similar to that of the aqueous sulfide fraction within 0.4 ‰ of 

S (Table 4).

505 Sulfur isotope data obtained in experiment m33 (Table 3, Fig. 5b,d) confirm the major isotope trends 506 for the SO

-H

S pair observed in m32. The isotope composition of sulfonate (O

-S-) and sulfane (-S) sulfur 507 of the initial thiosulfate rapidly evolves upon heating to 300°C, with sulfate and sulfide becoming with time 508

S-enriched and

S-depleted, respectively. The resulting 1000×ln

value is almost constant over the run 509 duration, yielding a steady state value of 20.1±1.5 ‰ (Fig. 5d).

510 In all performed experiments, the values of Δ

S for all species vary between -0.02 ‰ and +0.08 ‰, 511 and do not show any systematic trends (Fig. 6, 7, A4.2). The values of Δ

S vary between -1‰ and +1‰

512 without displaying any systematic trends amongst sulfide, sulfate and S

, and overlapping with those of the 513 initial thiosulfate. The scatter is mostly due to analytical issues because the analysis of 

S would commonly 514 be affected by a small contribution of fluorocarbon compounds that shifts measured 

S towards more 515 positive values (Rumble and Hoering, 1994). Nevertheless, these relatively small variations imply that there 516 is no significant sulfur mass independent fractionation on both

S and

S; however, they do provide 517 additional insight into both equilibrium and kinetic processes affecting mass-dependent fractionation among 518 the sulfur species as will be discussed in section 4.2.4.

519

520 4. DISCUSSION

521 4.1. Solubility and chemical speciation of sulfur

522

523 Sulfur solubility and species concentrations measured in this study can be compared with equilibrium

524 thermodynamic calculations. In all experiments, four major types of S chemical forms predicted by the

525 available thermodynamics (Table A2.1) are aqueous sulfate (SO

, HSO

, KSO

, and KHSO

), sulfide

526 (H

S, HS

, and KHS

), radical ions (S

at all T, and S

at 450°C), and pyrite (FeS

). In addition, in m22

527 aqueous SO

and three other phases, S

, at step m22/1, and barite (BaSO

) and alunite (KAl

(SO

)

(OH)

)

528 at step m22/2 after pyrite precipitation were predicted to form (Table 1). All other known solid phases are

529 predicted to be largely undersaturated in our experiments. Other types of aqueous species, such as thiosulfate,

530 S

, and traditional polysulfide ions, represent a negligibly small amount of S

at equilibrium (<0.1%).

531 Comparisons between calculated and measured concentrations of sulfate, sulfide, SO

and S

/ S

/ S

are 532 shown in Fig. 4; they reveal several interconnected points of discrepancy regarding the precipitation of the 533 K

SO

solid (in m32), sulfate-sulfide-pyrite equilibration, and the formation of S

, which are discussed 534 below.

535

536 4.1.1. K

SO

(s) precipitation

537 The precipitation of K

SO

(s) was inferred in run m32 (0.5 m K

S

O

-KOH-HCl, at 300 and 450°C 538 with in-situ changes in pH induced by HCl injection), through observation of concomitant decrease of total 539 dissolved potassium and sulfur concentrations through time (Fig. 3c, Appendix A3). The precipitation of 540 K

SO

(s) is, however, not consistent with equilibrium calculations using the thermodynamic properties of 541 K

SO

(s), K

and sulfate aqueous species from available data sources (Table A2.1). The calculations predict 542 K

SO

(s) to be undersaturated in the fluid by a factor of 10. The likely reason for this discrepancy is poor 543 constraints on the thermodynamic parameters of the dominant KSO

ion pair (Fig. 1), which are based on 544 HKF-model extrapolations relying on limited experimental data at low temperatures. To account for 545 K

SO

(s) formation, a correction to the value of the formation constant of KSO

from K

and SO

at 450°C 546 and 700 bar has been made to match the measured solubility of K

SO

(s) at each 450°C step of experiment 547 m32 (log K

= 3.4±0.5; Appendix A3). This correction does not exceed 1 log unit compared to the 548 SUPCRT original value (log K

= 4.4). The difference is within realistic uncertainties of HKF model 549 predictions for such ion pairs at elevated temperatures (e.g., Pokrovski et al., 1995; Scheuermann et al., 2019).

550 The 300°C step of this experiment does not allow direct reliable corrections for KSO

formation constant, 551 because no steady state has been attained (Fig. 3c). Therefore, we have corrected the fluid composition at the 552 300°C step of m32 by subtracting manually the mass-balance deduced amount of precipitated K

SO

, but 553 this correction has again a minor effect (Fig. A3.2). Nevertheless, to maintain consistency, in the following 554 discussion both 300°C and 450°C corrections were included when modeling equilibrium S speciation in 555 experiment m32 (Fig. 4c).

556

557 4.1.2. Aqueous sulfate and sulfide and pyrite

558 Before the pyrite precipitation stage, a decent agreement between measured and calculated S

559 values is observed for the least-concentrated experimental compositions in m29/1 (0.2 m K

S

O

, pH ~7.3,

560 350°C) and m33/3 (0.2m K

S

O

, pH ~5.3, 300°C). The other experimental compositions show

561 systematically lower measured S

, which is due to the presence of S

, as directly confirmed by mass

562 balance calculations and analyses of hexane extracts (discussed in section 4.1.3 below). Another potential

563 cause of the difference between measured and calculated S

in the highest-temperature run (450°C,

564 m32/2,3) might be an underestimation of the thermodynamically predicted amount of S

forming at the

565 expense of H

S. The measured S

concentrations in experiments m22, m29, m33 (and m32 at 450°C, after

566 correction for K

SO

(s)) agree within errors with the calculated ones, which further confirms that S

forms

567 more at the expense of sulfide than sulfate. An exception to this trend is stage m32/1 at 300°C and alkaline